On the memory function for the dynamic structure factor of interacting brownian particles

Cichocki, B.; Heß, W.

doi:10.1016/0378-4371(87)90176-2

Cited by 103 publications

(115 citation statements)

References 11 publications

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“…This is consistent with the exact equation expressing the timederivative of intermediate scattering function F (k; t) in terms of M irr (k; t) [27,28,32]. Namely, it follows from this equation that if the scattering function has a nonzero limit, lim t→∞ F (k; t) = F (k) > 0, then the irreducible memory function also has a non-zero limit,…”

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confidence: 83%

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Breakdown of a renormalized perturbation expansion around mode-coupling theory of the glass transition

Szamel¹,

Flenner²,

Hayakawa³

2013

EPL

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PACS 64.70.Q--Theory and modeling of the glass transition PACS 64.70.P--Glass transitions of specific systems PACS 61.20.Lc -Time-dependent properties; relaxation Abstract -We analyze a renormalized perturbation expansion around the mode-coupling theory of the glass transition. We focus on the long-time limit of the irreducible memory function. We discuss a renormalized diagrammatic expansion for this function and re-sum two infinite classes of diagrams. We show that the resulting contributions to the irreducible memory function diverge at the mode-coupling transition. A further re-summation of ladder diagrams constructed by iterating these divergent contributions gives a finite result which cancels the mode-coupling theory's expression for the irreducible memory function.

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confidence: 83%

“…Using a projection operator approach one can derive an exact but formal equation for M irr , which involves the socalled irreducible evolution operator that has single particle dynamics projected out [28]. It was showed in Ref.…”

mentioning

confidence: 99%

Breakdown of a renormalized perturbation expansion around mode-coupling theory of the glass transition

Szamel¹,

Flenner²,

Hayakawa³

2013

EPL

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“…This is achieved with a second projection step following Cichocki and Hess [78], see also Refs. [34,36,38].…”

Section: Second Projection Stepmentioning

confidence: 99%

Nonequilibrium fluctuation-dissipation relations of interacting Brownian particles driven by shear

Krüger

Fuchs

2010

Phys. Rev. E

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We present a detailed analysis of the fluctuation dissipation theorem (FDT) close to the glass transition in colloidal suspensions under steady shear using mode coupling approximations. Starting point is the manyparticle Smoluchowski equation. Under shear, detailed balance is broken and the response functions in the stationary state are smaller at long times than estimated from the equilibrium FDT. An asymptotically constant relation connects response and fluctuations during the shear driven decay, restoring the form of the FDT with, however, a ratio different from the equilibrium one. At short times, the equilibrium FDT holds. We follow two independent approaches whose results are in qualitative agreement. To discuss the derived fluctuation dissipation ratios, we show an exact reformulation of the susceptibility which contains not the full Smoluchowski operator as in equilibrium, but only its well defined Hermitian part. This Hermitian part can be interpreted as governing the dynamics in the frame comoving with the probability current. We present a simple toy model which illustrates the FDT violation in the sheared colloidal system.

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“…denotes the canonical ensemble average; the equilibrium distribution stands to the right of the quantity being averaged, and all operators act on it as well as on everything else. Usually, the memory function representation of the Laplace transform of the density correlation function, F (k; z), is written as [20] …”

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Colloidal Glass Transition: Beyond Mode-Coupling Theory

Szamel

2003

Phys. Rev. Lett.

132

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A new theory for dynamics of concentrated colloidal suspensions and the colloidal glass transition is proposed. The starting point is the memory function representation of the density correlation function. The memory function can be expressed in terms of a time-dependent pair-density correlation function. An exact, formal equation of motion for this function is derived and a factorization approximation is applied to its evolution operator. In this way a closed set of equations for the density correlation function and the memory function is obtained. The theory predicts an ergodicity breaking transition similar to that predicted by the mode-coupling theory, but at a higher density.PACS numbers: 82.70. Dd, 64.70.Pf, 61.20.Lc There has been a lot of interest in recent years in the theoretical description of dynamics of concentrated suspensions and the colloidal glass transition [1]. It has been stimulated by ingenious experiments which provide detailed information about microscopic dynamics of colloidal particles [2]. Due to the abundance of experimental data the colloidal glass transition has emerged as a favorite, model glass transition to be studied [3].One of the conclusions of these studies is the acceptance of the mode-coupling theory (MCT) as the theory for dynamics of concentrated suspensions and their glass transition [4]. Historically, this is somewhat surprising since MCT was first formulated for simple fluids with Newtonian dynamics [5] and only afterwards was adapted to colloidal systems with stochastic (Brownian) dynamics [6]. On the other hand, basic approximations of MCT are less severe for Brownian systems [7].MCT is a theory for correlation functions of slow variables, i.e. variables satisfying local conservation laws. For Brownian systems there is only one such variable: local density. MCT's starting point is the memory function representation of the density correlation function [8,9]. The memory function is expressed in terms of a timedependent pair-density (i.e. four-particle) correlation function evolving with so-called projected dynamics. For Brownian systems this step is exact [10]. The central approximation of MCT is the factorization approximation in which the pair-density correlation function is replaced by a product of two time-dependent density correlation functions. As a result one obtains a closed, nonlinear equation of motion for the density correlation function. This equation predicts an ergodicity breaking transition that is identified with the colloidal glass transition. MCT has also been used to describe, e.g., linear viscoelasticity [11], dynamics of sheared suspensions [12], and colloidal gelation [13]. By and large, its predictions agree with experimental and simulational results [4,14].In spite of these successes, MCT's problems are well known [4]. The most important, fundamental problem is that once the factorization approximation is made there is no obvious way to extended and/or improve the theory. This is most acute for Brownian systems because there the density is the...

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On the memory function for the dynamic structure factor of interacting brownian particles

Cited by 103 publications

References 11 publications

Breakdown of a renormalized perturbation expansion around mode-coupling theory of the glass transition

Breakdown of a renormalized perturbation expansion around mode-coupling theory of the glass transition

Nonequilibrium fluctuation-dissipation relations of interacting Brownian particles driven by shear

Colloidal Glass Transition: Beyond Mode-Coupling Theory

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